Debt and Cost of Capital
Kerry Back

Overview
- Adding debt increases enterprise value because of the tax savings, up to a point.
- Enterprise value is free cash flow discounted at the WACC.
- Debt and interest do not affect free cash flow.
- So adding debt must reduce the WACC.
- The effect is through taxes, not just because debt is cheaper capital.
If there were no taxes …
- WACC = % equity \(\times\) cost of equity + % debt \(\times\) cost of debt
- Consider all equity firm that switches to part debt. Perpetuity model.
- Example: equity value = enterprise value = $100, so expected free cash flow / cost of equity = $100.
- Issue riskless debt paying $1 per year in perpetuity at risk-free rate of 5%.
- Market value of debt is $1 / 0.05 = $20
- Use $20 to repurchase shares. Firm is now $80 equity and $20 debt.
- WACC is 0.8 \(\times\) new cost of equity + 0.2 \(\times\) 0.05.
- Claim: WACC is equal to old cost of equity
- This means cost of equity rises with leverage to offset use of cheaper debt capital.
- Example: old cost of equity is 11%.
- Claim: 0.8 \(\times\) new cost of equity + 0.2 \(\times\) 0.05 = 0.11.
- This means new cost of equity is 12.5%.
- Why?
- All risk piled on $80 of equity instead of $100 means equity risk per dollar is 10/8 of what it used to be.
- Risk premium should be 10/8 of what it used to be.
- Old risk premium was 11% - 5% = 6%
- New risk premium is (10/8) \(\times\) 6% = 7.5%
- New cost of equity is 5% + 7.5% = 12.5%.